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Seismic analysis generally is a dynamic analysis which may be linear or nonlinear while pushover is a nonlinear static analysis. The difference is in Pushover you try to get the capacity of the building for maximum displacement and in seismic analysis you try to keep your displacements under control as per codes.

Pushover is generally performed for retrofitting purposes where the building is old and you are doing some rehabilitating work. And many times in case of 10-12 story regular building. But as pushover is a static analysis and it does not capture the torsional effects accurately it is avoided for irregular buildings. Today all the computers can quickly perform linear dynamic analysis and it takes about 30-40 seconds to run it. So why not capture the dynamic effects for new buildings? That is why pushover analysis is slowly drifting away from design of new buildings.

As per i know from my undergrad thesis, the main basic difference between the pushover analysis and Time history analysis is that, in pushover analysis, the earthquake magnitude(accelerogram) is generated by the ETABS software. We have no control on it to create this artificial lateral load. We can not modify any factor for observing variable phenomena. On the other hand in time history analysis, a real life earthquake is chosen. It can be applied in any point with some factorization for real time observation. That's it.

In case of pushover, SAP can be the best option and but ETABS (latest version) is chosen for time history analysis. Because our latest BNBC code can be followed in the latest version making factor(c,k) changed.